[As a small pre-script, I think it is really exciting to see all this
talk about language design (both theoretical and practical). I've been
lurking on the CAML list (and the labeling thread) for a while,
trying to make sense of all of the discussion.]
Unless I am missing something, I don't see how you can reconcile
normal function application with commuting labeled arguments within
the current type system. Consider:
let sub_1 x y = <fun> : int -> int -> int
let sub_2 ~x ~y = <fun> : x:int -> y:int -> int
The function sub_1 is a normal curried function that builds a closure
as the arguments are applied, and then passes the arguments all at
once to the underlying function. The underlying closure data
structure can be thought of as an array since accesses are done via
position.
The function sub_2 is special. It seems as if the labels "x" and "y"
are part of the type of the argument. So, x:int is really a sub-type
of int. But if this is the case, then "x:int" and "y:int" have
different types. (Which certainly is consistent with how CAML handles
application of labeled arguments).
So, with commuting arguments, the given function signature doesn't
really give the whole story, we're really created two functions:
x:int -> y:int -> int
y:int -> x:int -> int
It seems to me that in order to support this type of argument
commuting, you end up creating the concept of a light-weight record
within the closure.
So, abstractly you end up with:
[x:int; y:int] -> int
and the syntax "sub_2 ~x:5" merely sets the "x" field of the
light-weight record held in the closure to the value 5. A call
"sub_2 ~y:10" would set the field "y" to 10. The special semantics of
this record are that when all the fields are set, it calls the
underlying function, and no field can be set twice.
This accumulation idea of values within the closure is equivalent to
the notion of the closure for sub_1 (since a call to "sub_1 5" sets
the 0th element in the array to the value 5). The difference is that
in the first case, the underlying closure structure is accessed as an
array, and in the second case it is accessed as a map.
The conclusion? These types of accesses *shouldn't* be mixed.
But they are... which is what I think is creating all the confusion.
In label mode, the "map" concept is the dominant one. In non-label
mode, the positional concept is dominant. In CAML, it seems that they
are unified by hacks, whereby in non-label mode a label can be
associated with each position, and if a label is given, it is checked
for accuracy. And, in label mode a position is assocated with each
label (based upon the order in which the arguments were declared) and
if no label is given the position can be used to do the mapping. But
in general, I think this unification is a bad idea... (e.g. label
mode's ability to commute labeled and unlabeled arguments!)
What is needed is either to choose one mode or the other (which cannot
be done -- as it seems that the one thing this discussion has agreed
on is that we can't agree on one particular mode). Or, a syntax
(yuck) needs to be created to allow function signatures to clearly
mark which closure access mode is dominant. Example:
f : [x:int; y:int] -> z:int -> int
The first two arguments are mapped primarily by name. Labels should
be used. The third argument is mapped by position. A label was
provided for clarity, but is not important. Possible applications:
f ~x:5 ~y:10 20
f ~y:18 ~x:2 17
f ~x:1 ~y:2 ~z:72
Unallowed applications:
f ~z:8 ~x:2 ~y:10 <- z is a positional arugment, not
interchangeable with the mapped arguments
it must come 3rd.
f 1 2 3 <- very bad style. this should probably not be
allowed, or at least a warning should be
thrown indicating that you should not access
the labeled argument "x" by position.
Note also that the currying works properly (and intuitively):
(f ~x:5) : [y:int] -> z:int -> int
(f ~y:10) : [x:int] -> z:int -> int
(f ~y:8 ~x:20) : z:int -> int
If you apply a labeled argument, it consumes on of the arguments from
the "[]".
-mike.
p.s. Does this make sense, or am I missing something in the theory?
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